To extract a backbone of a given size from a temporal network data set, we consider the Significant Ties (ST) filter
[1]}. In this method, the actual number of
temporal edges between two nodes is compared to the one
of a temporal null model. The significant ties at significance level \(\alpha \)  are the ones such that their number of temporal edges cannot be explained by the null model at significance level \(\alpha \) . Specifically, the null model is defined
as follows:
an “activity level” \(a_i\)  is associated to each node \(i\) , and two nodes \(i\)  and \(j\)  have a temporal edge at each time with probability \(a_i a_j\) . The activity levels of the nodes are obtained from the data by maximum likelihood estimation (see Methods and kobayashi2019structural).
Tuning \(\alpha \)  makes it possible to select backbones representing a specific fraction \(f\)  of the ties of the original data.
